Simplify. Rewrite the expression in the form $y^n$. $\dfrac{y^{5}}{y^3}=$
$\begin{aligned} \dfrac{y^{5}}{y^3}&=y^{5-3} \\\\ &=y^2 \end{aligned}$ This follows from the general rule $\dfrac{x^m}{x^n}=x^{m-n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} \dfrac{y^{5}}{y^3}&=\dfrac{\overbrace{\cancel y\cdot \cancel y\cdot \cancel y\cdot y\cdot y}^\text{5 times}}{\underbrace{\cancel y\cdot \cancel y\cdot \cancel y}_\text{3 times}} \\\\\\ &=\underbrace{y\cdot y}_\text{2 times} \\\\ &=y^2 \end{aligned}$ In conclusion, $\dfrac{y^{5}}{y^3}=y^2$.